At George Washington High School, the ratio of graduating seniors that go on to college compared to those who do not is 7:4. Last year, 28 students did not go on to college. How many students did?

Jun 20, 2018

Number of seniors that graduated is $49$

Explanation:

You can get the answer in two ways..

Method 1

Comparing the given..

$7 : 4 \to \text{ratios}$

$7 \to$ Graduated seniors..

$4 \to$ Seniors that was unable to graduate..

$28 \to$ Number Seniors that was unable to graduate..

$x \to$ Number of Seniors that graduated..

Hence comparing;

$\frac{4}{28} = \frac{7}{x}$

Cross multiplying;

$4 \times x = 7 \times 28$

$4 x = 196$

$x = \frac{196}{4}$

$x = 49$

Therefore, the number of seniors that graduated is $49$

Method 2

Using Ratios and Proportions..

Sum of their ratios is $7 + 4 = 11$

Looking for the total number of seniors;

$28 = \frac{4}{11} \times y$

Where, $y$ represents the total number of seniors..

$28 = \frac{4}{11} y$

Dividing both sides by $\frac{4}{11}$

$28 \div \frac{4}{11} = \frac{\frac{4}{11} y}{\frac{4}{11}}$

$28 \div \frac{4}{11} = \frac{\cancel{\frac{4}{11}} y}{\cancel{\frac{4}{11}}}$

$28 \times \frac{11}{4} = y$

${\cancel{28}}^{7} \times \frac{11}{\cancel{4}} ^ 1 = x$

$7 \times 11 = y$

$y = 77$

Now to find the number of seniors that graduated..

Let, $x$ represent the number of seniors that graduates;

$x = \frac{7}{11} \times 77$

$x = \frac{7}{\cancel{11}} ^ 1 \times {\cancel{77}}^{7}$

$x = 7 \times 7$

$x = 49$

Therefore the number of seniors that graduated is $49$